The external Pirani gauge is in series with a constant-current barretter in two adjacent arms of a Wheatstone bridge. Resistances comprise the other two arms.
The bridge is initially balanced before starting the vacuum pump/s
When the Pirani gauge wire changes resistance, the voltage along it varies, since the current flowing is constant. This change in voltage unbalances the bridge, and the difference is read off the meter on the front panel.
The meter scale is calibrated in mm Hg correspondingly.